Existence of three solutions for a higher-order boundary-value problem

John R. Graef, Lingju Kong, Qingkai Kong
Abstract:
We consider a higher-order multi-point boundary-value problem with
a nonlinear boundary condition.
Sufficient conditions are obtained for the existence of three solutions.
In our problem, the differential equation has dependence on all
lower order derivatives of the unknown function and the boundary
condition covers many multi-point boundary conditions studied
earlier by other authors. Our results extend some recent work
in the literature.